A Wheatstone bridge
is a measuring instrument
invented by Samuel Hunter Christie
and improved and popularized by Sir Charles Wheatstone
. It is used to measure an unknown electrical resistance
by balancing two legs of a bridge circuit
, one leg of which includes the unknown component. Its operation is similar to the original potentiometer
except that in potentiometer circuits the meter used is a sensitive galvanometer
In the circuit on the right, is the unknown resistance to be measured; , and are resistors of known resistance and the resistance of is adjustable. If the ratio of the two resistances in the known leg is equal to the ratio of the two in the unknown leg , then the voltage between the two midpoints (B and D) will be zero and no current will flow through the galvanometer . is varied until this condition is reached. The current direction indicates whether is too high or too low.
Detecting zero current can be done to extremely high accuracy (see galvanometer). Therefore, if , and are known to high precision, then can be measured to high precision. Very small changes in disrupt the balance and are readily detected.
At the point of balance, the ratio of
Alternatively, if , , and are known, but is not adjustable, the voltage or current flow through the meter can be used to calculate the value of , using Kirchhoff's circuit laws (also known as Kirchhoff's rules). This setup is frequently used in strain gauge and Resistance Temperature Detector measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.
First, Kirchhoff's first rule is used to find the currents in junctions B and D:
Then, Kirchhoff's second rule is used for finding the voltage in the loops ABD and BCD:
The bridge is balanced and , so the second set of equations can be rewritten as:
Then, the equations are divided and rearranged, giving:
From the first rule, and . The desired value of is now known to be given as:
If all four resistor values and the supply voltage () are known, the voltage across the bridge () can be found by working out the voltage from each potential divider and subtracting one from the other. The equation for this is:
This can be simplified to:
The Wheatstone bridge illustrates the concept of a difference measurement, which can be extremely accurate. Variations on the Wheatstone bridge can be used to measure capacitance
and other quantities, such as the amount of combustible gases in a sample, with an explosimeter
. The Kelvin double bridge
was specially adapted from the Wheatstone bridge for measuring very low resistances. A "Kelvin one-quarter bridge" has also been developed. It has been theorized that a "three-quarter bridge" could exist; however, such a bridge would function identically to the Kelvin double bridge.
The concept was extended to alternating current measurements by James Clerk Maxwell in 1865 and further improved by Alan Blumlein in about 1926.
Modification of the fundamental bridge
The Wheatstone bridge is the fundamental bridge, but there are other modifications that can be made to measure various kinds of resistances when the fundamental Wheatstone bridge is not suitable. Some of the modifications are: